The GNSS Evolutionary Architecture Study (GEAS) Panel has been evaluating future GNSS-based architectures to provide worldwide instrument approach guidance known as LPV-200 in the 2025 to 2030 time frame. One of the architectures being considered by GEAS is based on a new concept called relative receiver autonomous integrity monitoring (RRAIM). In this architecture RRAIM is implemented in aircraft and is used in conjunction with a system like the satellite-based augmentation system (SBAS), possibly with a reduced number of ground reference stations or an integrity-assured GPS III system that meets all LPV-200 requirements except for the integrity time-to-alert (TTA) requirement. RRAIM fills the time gap between the required TTA and the TTA assured by GPS III (or SBAS augmentation) by propagating the most recent integrity-assured position solution to the current time using accumulated carrier phase single differences of range measurements. RRAIM gives significantly higher service availability than can be obtained with stand-alone absolute RAIM (ARAIM). This paper develops a position domain RRAIM method with an optimization scheme that further improves LPV-200 service availability.